An algebraic quantum field theoretic approach to toric code with gapped boundary
An algebraic quantum field theoretic approach to toric code with gapped boundary
复制标题
DOI：
10.1063/5.0149891
复制
发表时间：
2022-12
影响因子：
1.3
通讯作者：
Daniel Wallick
中科院分区：
文献类型：
--
作者：
Daniel Wallick
拓扑有序的量子自旋系统已成为人们非常感兴趣的领域，因为它们可以提供量子计算的容错手段。这种自旋系统最简单的例子之一是基塔耶夫的环面码。 Naaijkens 通过代数量子场论使用算子代数方法，对无限平面晶格（热力学极限）上的环面码进行了严格的数学处理。我们采用他的方法来研究具有间隙边界的环面码的情况。特别是，我们恢复了 Kitaev 和 Kong 中描述的凝聚结果，并表明边界理论是整体上的模张量类别，正如预期的那样。
Topologically ordered quantum spin systems have become an area of great interest, as they may provide a fault-tolerant means of quantum computation. One of the simplest examples of such a spin system is Kitaev’s toric code. Naaijkens made mathematically rigorous the treatment of toric code on an infinite planar lattice (the thermodynamic limit), using an operator algebraic approach via algebraic quantum field theory. We adapt his methods to study the case of toric code with gapped boundary. In particular, we recover the condensation results described in Kitaev and Kong and show that the boundary theory is a module tensor category over the bulk, as expected.